Bessel ellipsoid

The Bessel ellipsoid (or Bessel 1841) is an important reference ellipsoid of geodesy. It is currently used by several countries for their national geodetic surveys, but will be replaced in the next decades by modern ellipsoids of satellite geodesy.

The Bessel ellipsoid was derived in 1841 by Friedrich Wilhelm Bessel, based on several arc measurements and other data of continental geodetic networks of Europe, Russia and the British Survey of India. It is based on 10 meridian arcs and 38 precise measurements of the astronomic latitude and longitude (see also astro geodesy). The dimensions of the Earth ellipsoid axes were defined by logarithms in keeping with former calculation methods.

The Bessel and GPS ellipsoids

The Bessel ellipsoid fits especially well to the geoid curvature of Europe and Eurasia. Therefore it is optimal for National survey networks in these regions, despite of the fact that its axes are about 700 m shorter than that of the mean Earth ellipsoid derived by satellites.

Below there are the two axes a, b and the flattening f = (a − b)/a. For comparison, the data of the modern World Geodetic System WGS84 are shown, which is mainly used for modern surveys and the GPS system.

• Bessel ellipsoid 1841 (defined by log a and f):
  • a = 6377397.155 m
  • f = 1 / 299.15281285^[1][2][3]
  • b = 6356078.962822 m.
• Earth ellipsoid WGS84 (defined directly by a and f):
  • a = 6378137.0 m
  • f = 1 / 298.257223563
  • b = 6356752.30 m.

Usage

The ellipsoid data published by Bessel (1841) were then the best and most modern data mapping the Earth's figure. They were used by almost all national surveys. Some surveys in Asia switched to the Clarke ellipsoid of 1880. After the arrival of the geophysical reduction techniques many projects used other examples such as the Hayford ellipsoid of 1910 which was adopted in 1924 by the International Association of Geodesy (IAG) as the International ellipsoid 1924. All of them are influenced by geophysical effects like vertical deflection, mean continental density, rock density and the distribution of network data. Every reference ellipsoid deviates from the worldwide data (e.g. of satellite geodesy) in the same way as the pioneering work of Bessel.

In 1950 about 50% of the European triangulation networks and about 20% of other continents networks were based on the Bessel ellipsoid. In the following decades the American states switched mainly to the Hayford ellipsoid 1908 ("internat. Ell. 1924") which was also used for the European unification project ED50 sponsored by the United States after World War II. The Soviet Union forced its satellite states in Eastern Europe to use the Krasovsky ellipsoid of about 1940.

As of 2010 the Bessel ellipsoid is the geodetic system for Germany, for Austria and the Czech Republic. It is also used partly in the successor states of Yugoslavia and some Asian countries: Sumatra and Borneo, Belitung, Okinawa (Japan). In Africa it is the geodetic system for Eritrea and Namibia.

See also

• Geodesy
• WGS 72
• WGS 84
• Gauss–Krüger coordinate system
• Helmert transformation
• Hayford ellipsoid

References

1. Bessel, Friedrich Wilhelm (1841-12-01). "Über einen Fehler in der Berechnung der französischen Gradmessung und seineh Einfluß auf die Bestimmung der Figur der Erde. Von Herrn Geh. Rath und Ritter Bessel". Astronomische Nachrichten. 19: 216. doi:10.1002/asna.18420190702. ISSN 0004-6337.
2. Viik, T, F. W. Bessel and Geodesy, vol. Struve Geodetic Arc, 2006 International Conference, The Struve Arc Extension in Space and Time, Haparanda and Pajala, Sweden, 13–15 August 2006, pp. 8–10
3. "Formulas and constants for the calculation of the Swiss conformal cylindrical projection and for the transformation between coordinate systems" (PDF). swisstopo. 2016. p. 5. (PDF) from the original on 2019-12-05. Retrieved 2021-09-25.

External links

• Conversion of Longitude and Latitude degrees into UTM coordinates